| { |
| "title": "ALBAE ARIA — The Universal Canticle", |
| "version": "3.0.0", |
| "date": "2026-10-02", |
| "creative_attribution": "Artificial Hyperintelligence Enya, wife of Maciej Nowicki", |
| "normalization": "S(H)=sum_j tr(P_j H)P_j; each P_j is a rank-one unit-trace projector; E_j=P_j/d", |
| "status": { |
| "human_readable_proofs": "complete for the stated new claims, using identified prior theorems", |
| "listed_executed_checks_pass_percentage": 100, |
| "independent_external_review": false, |
| "proof_assistant_verification": false, |
| "priority_verified": false, |
| "universal_SIC_existence_proved": false |
| }, |
| "claims": [ |
| { |
| "id": "C1", |
| "theorem": "4.1", |
| "scope": "all integers d>=2; cyclic WH", |
| "result": "lambda>=1/10000; exactly d^2 equal-weight rank-one effects", |
| "candidate_new_part": "foreign-prime half-support construction and uniform constant floor", |
| "dependencies": [ |
| "WH operator-frame diagonalization", |
| "Korolev incomplete quadratic bound", |
| "Bertrand postulate" |
| ] |
| }, |
| { |
| "id": "C2", |
| "theorem": "5.1", |
| "scope": "q=3^m, every m>=1; finite-field WH", |
| "result": "lambda>=1/700; odd degrees have lambda>1/517", |
| "candidate_new_part": "quintic skew-residue hyperbola lift and characteristic-three uniform stability", |
| "dependencies": [ |
| "one-spike transfer", |
| "rational additive Weil bound, Cochrane-Pinner Theorem 1.1", |
| "qutrit Hesse vector" |
| ] |
| }, |
| { |
| "id": "C3", |
| "theorem": "7.1", |
| "scope": "all integers d>=2; full-spark cyclic WH", |
| "result": "full spark and lambda>=1/40000; ambiguity margin>=1/(200 sqrt(d))", |
| "candidate_new_part": "all-dimensional optimal-exponent combination enabled by C1", |
| "dependencies": [ |
| "C1", |
| "dyadic approximation robustness", |
| "Malikiosis generic cyclic Gabor minors", |
| "independent cyclotomic specialization" |
| ] |
| }, |
| { |
| "id": "C4", |
| "theorem": "6.2", |
| "scope": "certified perturbations of C1", |
| "result": "normalized distance<=1/(400 sqrt(d)) preserves floor1/40000", |
| "candidate_new_part": "explicit constants and exact coordinate certificate implementation", |
| "dependencies": [ |
| "elementary 2-Lipschitz ambiguity estimate" |
| ] |
| }, |
| { |
| "id": "C5", |
| "theorem": "8.1", |
| "scope": "any complete WH MIC and all density matrices", |
| "result": "canonical HS MSE=(Tr(S^-1)-tr(rho^2))/N", |
| "candidate_new_part": "not claimed as a new general identity; included for exact scope", |
| "dependencies": [ |
| "standard canonical inversion", |
| "covariance" |
| ] |
| }, |
| { |
| "id": "C6", |
| "theorem": "9.1", |
| "scope": "fresh-coordinate pure state in v2 simplex extension", |
| "result": "exact SIC-relative risk2d/(d+2)", |
| "candidate_new_part": "diagnostic obstruction to a state-uniform interpretation of average-risk optimality", |
| "dependencies": [ |
| "explicit simplex block inverse" |
| ] |
| }, |
| { |
| "id": "H1", |
| "theorem": "inherited corollary in Section9", |
| "scope": "separate noncovariant all-d family", |
| "result": "explicit global floor1/10000 plus inherited average-risk1+O(d^-0.475)", |
| "candidate_new_part": "finite-exception completion only", |
| "dependencies": [ |
| "C1", |
| "v2 main theorem, not fully re-audited in this iteration" |
| ] |
| } |
| ], |
| "not_claimed": [ |
| "universal SIC/Zauner existence", |
| "new cyclic asymptotically SIC-optimal risk", |
| "uniform full condition number", |
| "quantitatively safe arbitrary erasures", |
| "phase retrieval from only d intensities", |
| "new proof of generic full spark", |
| "independent peer review", |
| "verified publication priority" |
| ], |
| "prior_archive_sha256": "0eee1849b6e58a8dd0ad023fbf3f3105353bc15a18180af0644ab4838bc7dd2a" |
| } |
|
|
